\begin{answer}{iszerocovarianceindependent}
No. The interviewer gave you the answer in the previous question
(although with different symbols)
and is probably checking whether you realised this.
The current question and the previous question are question \ref{q:iszerocorrelationindependent} split in two.
Construct the same scenario as in question \ref{q:constructzerocorrelation}, but change the symbols to those of the new question.
That is, let
\begin{align*}
P(Z = -1) &= 0.5  \\
P(Z =  1) &= 0.5
\end{align*}
and
$X \sim \text{Normal}(0,1)$, and
$Y = ZX$,
and then calculate
\begin{align*}
\Cov(X,Y)
&= \Cov(X, ZX) \\
&= \E(XZX) - \E(X) \E(ZX)  \\
&= \E(X^2 Z) - \E(X) \E(ZX)  \\
&= \E(X^2) \E(Z) - \E(X)\E(Z)\E(X)   \quad \text{independence} \\
&=  0                                \quad \text{since } E(Z)=0
\text{.}
\end{align*}
There is a very clear dependence between $X$ and $Y$, but their covariance is zero.
\end{answer}
